For a ?novice? at this board, you have made an astute observation. Education tends to be dominated by a simplified discussion about complex problems (reminds me of politics!).

Relative to this particular thread, I was just thinking earlier today that we are in danger of being de-professionalized by current movements (not just one) which emphasize students figuring things out with resources as opposed to an instructor designing an effective sequence of experiences. There are plenty of policy makers who would be happy to get rid of most instructor/teacher contact, and make us into tutors and support staff. We need to keep the profession in our work, and keep our work professional.

Direct instruction can work well - for some students, generally those who don't need much support. There's a good deal of excellent research (by pseudo-researchers?)at NSF and IES to support the idea that a teacher talking at kids is not an effective way for ALL students to learn.

On the other hand, the teacher can't just hand the kid a problem and step back. Good math teaching is complex and involves getting kids to do math in meaningful ways. There's quite a bit written on this by both classroom teachers and by researchers.

I'm new to these forums but I'm kind of surprised on people writing in them try to simplified complex issues and then proceed to demonize one side of them. Is this what passes for discourse?